《电路》（英文版）14-6 Effective values and power

8 14-6 Effective values and power The effective or rms value of the function f(t) is f (tdt 2 0+>an cos nat+bn sin nax )=a0+ 2cn cos(nar-9mn TJ0/,40+ ∑ Cn cos(nat 20/ ∑ C2/2=√c+c2/2+c2/2+… If(2)=V+∑ 2v sin(nat-p i0)=10+∑√2 In sin(nat-n) n=1 V=V+2+V2+…mdl=+2+l2+

§14-6 Effective values and power The effective or rms value of the function f(t) is  = T rms f t dt T F 0 2 ( ) 1 ( )   =  = = + + = + − 1 0 1 0 cos( ) 2 1 cos sin 2 1 ( ) n n n n n n f t a a nt b nt a c nt             = + −  = T n rms a c n n t n dt T F 0 2 1 0 cos( ) 2 1 1    + = + + +      =   = / 2 / 2 / 2 2 1 2 2 2 1 2 0 1 2 2 0 a c c c c n n . 2 2 2 1 2 0 2 2 2 1 2 V = V0 +V +V + and I = I + I + I +   = = + − 1 0 ( ) 2 sin( ) n n n  i t I I nt   = = + − 1 0 ( ) 2 sin( ) n n n If  t V V nt 

The instantaneous power P=D=0+∑√2 nsin(nat+n)o+∑√2 Insin(ne+wn) H=1 n= The average power P=rm=W+210a+9)n+22m(m+Wn) 1= n =V0I0+ ∑ nn (n-n)+∑ V.I. cos.9 H=1 n=1 =V0l0+11c091+2l2C0s82+…(n=pn-n

The instantaneous power p = .i =[ 2 sin( )] 1 0   = + + n n n V V nt  [ 2 sin( )] 1 0   = + + n n n I I nt  The average power   = = T T T pdt T P 0 0 1 1 [ 2 sin( )] 1 0   = + + n n n V V nt  I I n t dt n n n [ 2 sin( )] 1 0   = +  +   = = + − 1 0 0 cos( ) n n n n n V I V I     = = + 1 0 0 cos n n n n V I V I  =V0 I 0 +V1 I 1 cos1 +V2 I 2 cos2 + ( ) n  n  n = −

P=V010+H1c0s91+2l2c0s2+…(n=gn-vn) 9.-- the angle on the equivalent impedance of the network at the angular frequency of no Vn, ln---the effective values of respective sine function In the special case of a single frequency sinusoidal voltage, Vo=V2-V3=.0 P=VI, cos 9 For a dc voltage Vi=v2=V3=.0 P=volo-VI

cos cos ... P =V0 I 0 +V1 I 1 1 +V2 I 2 2 + ( ) n  n  n = − the angle on the equivalent impedance of the network at the angular frequency of . n − − n Vn , In ---the effective values of respective sine function. In the special case of a single frequency sinusoidal voltage, V0=V2=V3=…=0 = 1 1 1 P V I cos For a dc voltage V1=V2=V3=…=0 P=V0 I0=VI